Nonlinear Schrِdinger equation with unbounded or decaying radial potentials involving exponential critical growth in

We study the existence and multiplicity of solutions for the following class of nonlinear Schrödinger equations − Δ u + V ( ∣ x ∣ ) u = Q ( ∣ x ∣ ) f ( u )  in R 2 , where V and Q are unbounded or decaying radial potentials and the nonlinearity f ( s ) has exponential critical growth. The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.